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# Wavy Line Method Application - Exercise Question #3

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Wavy Line Method Application - Exercise Question #3  [#permalink]

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26 Aug 2016, 02:36
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Wavy Line Method Application - Exercise Question #3

List the negative integral values of x that render the algebraic expression $$(x – 5)^8 (x – 2)^3$$ positive.

Wavy Line Method Application has been explained in detail in the following post:: http://gmatclub.com/forum/wavy-line-method-application-complex-algebraic-inequalities-224319.html

Detailed solution will be posted soon.
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Re: Wavy Line Method Application - Exercise Question #3  [#permalink]

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26 Aug 2016, 09:58
EgmatQuantExpert wrote:
Wavy Line Method Application - Exercise Question #3

List the negative integral values of x that render the algebraic expression $$(x – 5)^8 (x – 2)^3$$ positive.

Wavy Line Method Application has been explained in detail in the following post:: http://gmatclub.com/forum/wavy-line-method-application-complex-algebraic-inequalities-224319.html

Detailed solution will be posted soon.

Question States we need to find out the value of negative integral values of x such that $$(x – 5)^8 (x – 2)^3$$ >0

Since the power of (x-5) is EVEN, we don't need to consider the negative values between 2 and 5.

Substituting the values of x as 2 and 5 on number line, we will get the range of x as (-infinity, 2).

Please correct me if I am missing anything.
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Re: Wavy Line Method Application - Exercise Question #3  [#permalink]

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04 Sep 2016, 23:54
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Hi Abhimahna,

For x=1, the expression is negative whereas we want the resultant expression to be positive.

In my opinion, there are no negative integral solutions for this expression to result in a positive number.

Please cross-check by plugging in negative values (x=-1,-2 and so on)
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Wavy Line Method Application - Exercise Question #3  [#permalink]

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04 Sep 2016, 23:59
Jurassic wrote:
Hi Abhimahna,

For x=1, the expression is negative whereas we want the resultant expression to be positive.

In my opinion, there are no negative integral solutions for this expression to result in a positive number.

Please cross-check by plugging in negative values (x=-1,-2 and so on)

Yes, you are correct. I missed such a simple thing. Thanks Jurassic Park

Your 1st Kudo will be given by me.
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Re: Wavy Line Method Application - Exercise Question #3  [#permalink]

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06 Sep 2016, 19:34
Zero points are 2 and 5. Plot them on the number line.

Start from x=5 (top right). Power of (x-5) is even. So, the wavy line should bounce back at x=5.

From the graph, for any number > 2, the algebraic expression remains positive. So, solution would be all integers >2 (not = 2 since at 2, the expression becomes 0)
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wavy line.PNG [ 6.41 KiB | Viewed 2769 times ]

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Re: Wavy Line Method Application - Exercise Question #3  [#permalink]

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08 Sep 2016, 23:42
Hi Rajaram,

The question asks for negative integral values of x. Hence, the solution of all integers > 2 will be incorrect in this case.
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Re: Wavy Line Method Application - Exercise Question #3  [#permalink]

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18 Nov 2016, 02:57
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Solution

Hey Everyone,

Please find below the solution of the given problem.

Rewriting the inequality to easily identify the zero points

We want the given algebraic expression to be positive.

So, we need to find the range of values of x for the following inequality:

$$(x – 5)^8 (x – 2)^3>0$$

After we find the range, we need to choose the negative integers in this range since the question asks for negative integral values that satisfy the above inequality.

Plotting the zero points and drawing the wavy line:

Required Range:

Per the wavy line drawn above, it is clear that 2 < x < 5 and x > 5 render the given expression positive.

However, question asks us to choose only negative integral values for x.
Note that these ranges do NOT contain any negative integers.

Therefore, no negative integral value exists for x such that the given expression can be rendered positive.

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Re: Wavy Line Method Application - Exercise Question #3  [#permalink]

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01 Feb 2017, 12:16
Payal : can u plz elaborate on the negative integral values for an expression in general
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Re: Wavy Line Method Application - Exercise Question #3  [#permalink]

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05 Aug 2018, 12:46
Sachin07 wrote:
Payal : can u plz elaborate on the negative integral values for an expression in general

Those negative integers (like -2, -3, -1..etc) for which the expression holds true. In this case, for all negative integers the expression is less than zero. Hence, there is no -ve integral / integer value for which expression is > 0 i.e positive.
Re: Wavy Line Method Application - Exercise Question #3 &nbs [#permalink] 05 Aug 2018, 12:46
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